Question

1. Without solving the equation, find the sum and product of its solutions.(a) x^2 + 7x - 11 = 0 b) 3x^2 - 5x - 9 = 0.

Answer 1

Given

The equation is given as

$\begin{gathered} a.x^2+7x-11=0 \\ b.3x^2-5x-9=0 \end{gathered}$Explanation

a. The equation is given as

$x^2+7x-11=0$

The general equation is

$ax^2+bx+c$

The sum of the root is determined as

$\frac{-b}{a}$

Substitute the values from the given equation.

$-\frac{b}{a}=-\frac{7}{1}$

The product of roots is determined as

$\frac{c}{a}$

Substitute the values from the given equation.

$\frac{c}{a}=-\frac{11}{1}=-11$

b. The equation is given

$3x^2-5x-9=0$

The sum of root is

$\frac{-b}{a}=-\frac{-5}{3}=\frac{5}{3}$

The product of root is

$\frac{c}{a}=-\frac{9}{3}=-3$Answer

a. The sum of root is -7.

The product of root is -11.

b. The sum of root is 5/3.

The product of root is -3.